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Dynamic stiffness matrix of a poroelastic multi-layered site and its Green’s functions

Liang Jianwen (梁建文) and You Hongbing (尤红兵)

Department of Civil Engineering, Tianjin University, Tianjin 300072, China

Abstract: Few studies of wave propagation in layered saturated soils have been reported in the literature. In this paper, a general solution of the equation of wave motion in saturated soils, based on one kind of practical Biot¡®s equation, was deduced by introducing wave potentials. Then exact dynamic-stiffness matrices for a poroelastic soil layer and half-space were derived, which extended Wolf's theory for an elastic layered site to the case of poroelasticity, thus resolving a fundamental problem in the field of wave propagation and soil-structure interaction in a poroelastic layered soil site. By using the integral transform method, Green's functions of horizontal and vertical uniformly distributed loads in a poroelastic layered soil site were given. Finally, the theory was verified by numerical examples and dynamic responses by comparing three different soil sites. This study has the following advantages: all parameters in the dynamic-stiffness matrices have explicitly physical meanings and the thickness of the sub-layers does not affect the precision of the calculation which is very convenient for engineering applications. The present theory can degenerate into Wolf’s theory and yields numerical results approaching those for an ideal elastic layered site when porosity tends to zero.

Keywords: Biot's equation; poroelastic layered site; dynamic-stiffness matrix; Green's function